Mark S. Drew and Amin Yazdani Salekdeh

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Multispectral Image Invariant to Illumination
Colour, Strength, and Shading

• Mark S. Drew and Amin Yazdani Salekdeh
• School of Computing Science,
• Simon Fraser University,
• Vancouver, BC, Canada
• mark/ayazdani_at_cs.sfu.ca

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Table of Contents

• Introduction
• RGB Illumination Invariant
• Multispectral Image Formation
• Synthetic Multispectral Images
• Measured Multispectral Images
• Conclusion

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Introduction

• Invariant Images RGB
• Information from one pixel, with calibration
• Information from all pixels use entropy
• New ?
• Multispectral data
• Information from one pixel without calibration,
  but knowledge of narrowband sensors peak
  wavelengths

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RGB Illumination Invariant
Removing Shadows from Images, ECCV 2002 Graham
Finlayson, Steven Hordley, and Mark Drew
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An example, with delta function sensitivities
RGB
Narrow-band (delta-function sensitivities)
Log-opponent chromaticities for 6 surfaces under
9 lights
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Deriving the Illuminant Invariant
RGB
Log-opponent chromaticities for 6 surfaces under
9 lights
Rotate chromaticities
This axis is invariant to illuminant colour
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An example with real camera data
RGB
Normalized sensitivities of a SONY DXC-930 video
camera
Log-opponent chromaticities for 6 surfaces under
9 different lights
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Deriving the invariant
RGB
Log-opponent chromaticities
Rotate chromaticities
The invariant axis is now only approximately
illuminant invariant (but hopefully good enough)
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Image Formation
Multispectral

• Illumination motivate using theoretical
  assumptions, then test in practice
• Plancks Law in Wiens approximation
• Lambertian surface S(?), shading is ?, intensity
  is I
• Narrowband sensors qk(?), k1..31, qk(?)?(?-?k)
• Specular colour is same as colour of light
  (dielectric)

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Multispectral Image Formation

• To equalize confidence in 31 channels, use a
  geometric-mean chromaticity
• Geometric Mean Chromaticity
• ?
• with

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Multispectral Image Formation
surface-dependent
sensor-dependent
illumination-dependent
So take a log to linearize in (1/T) !
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Multispectral Image Formation

• Logarithm

known because, in special case of multispectral,
know ?k !
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Multispectral Image Formation

• If we could identify at least one specularity, we
  could recover log ?k ??
• ?Nope, no pixel is free enough of surface colour
  ?.
• So (without a calibration) we wont get log ?k,
  but instead it will be the origin in the
  invariant space.
• Note Effect of light intensity and shading
  removed 31D ? 30-D
• Now lets remove lighting colour too we know
  31-vector (ek eM) ? (-c2/?k - c2/?M)
• Projection ? to (ek eM) removes
  effect of light, 1/T 30D ? 29-D

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Algorithm
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Algorithm

• Whats different from RGB? ?
• For RGB have to get lighting-change direction
• (ek eM) either from
• calibration, or
• internal evidence (entropy) in the image.
• For multispectral, we know (ek eM) !

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First, consider synthetic images, for
understanding
Surfaces 3 spheres, reflectances from Macbeth
ColorChecker
Camera Kodak DSC 420
31 sensor gains qk(?)
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Synthetic Images
shading, for light 1, for light 2
Under blue light, P10500
Under red light, P2800
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Synthetic Images
Original not invariant
Spectral invariant
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Measured Multispectral Images
Under D75
Under D48
Invt. 1
Invt. 2
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Measured Multispectral Images
In-shadow, In-light
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Measured Multispectral Images
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Measured Multispectral Images
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Measured Multispectral Images
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Conclusion

• A novel method for producing illumination
  invariant, multispectral image
• Successful in removing effects of
• Illuminant strength, colour, and shading

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